Domain authority is one of the most difficult metrics to influence.
Good quality inbound links from sites with good domain authority and mozTrust is one of the biggest factors in increasing domain auth, therefore you should consider the following....
1. Build good content, i'm sure you have read it a thousand times before on here and many other forums, but good quality content and being active through social channels is by far the best and most sustainable way of building inbound links and ultimately influencing domain auth.
2. Ensure you are listed with the "good" directories such as DMoz, Yelp, Yahoo etc, these are no where near as powerful in terms of link juice as they once were, but you should still be on them.
3. Embark on a traditional link building strategy, but ensuring you don't build spammy links and ensure you have anchor text diversity (ie don't try and keyword stuff anchor text)
4. Use tools such as SEOmoz's newly acquired followerwonk to find influencers in your industry who are likely to be interested in your site and connect and interact with them to see if you can get them to link/retweet your content.
Of the above the biggest gain for the least amount of work is likely to be item 2, registering with directories, but sadly there is no magic bullet for increasing domain auth, but then again, if there was, everyone would be doing it!!
You may also want to check out the SEOmoz explanation of "what is domain authority?" for an indepth explanation of how domain auth is calculated.
http://www.seomoz.org/learn-seo/domain-authority
Hope that helps
Justin